Which of the following functions has a graph that approaches but never touches t

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Question: Which of the following functions has a graph that approaches but never touches the x-axis?

Options:

Correct Answer: Exponential function

Solution:

An exponential function approaches the x-axis as x approaches negative infinity but never actually touches it.

Which of the following functions has a graph that approaches but never touches the x-axis?

Which of the following functions has a graph that approaches but never touches the x-axis?

Step 1: Understand what the x-axis is. The x-axis is the horizontal line on a graph where the value of y is 0.
Step 2: Learn about functions. A function is a rule that assigns each input (x) to exactly one output (y).
Step 3: Identify what it means for a graph to approach the x-axis. This means that as the x-values get very large or very small, the y-values get closer to 0 but never actually reach 0.
Step 4: Look at different types of functions. Some functions, like linear functions, can cross the x-axis, while others, like exponential functions, do not.
Step 5: Focus on exponential functions. An exponential function has the form y = a * b^x, where a is a constant, b is a positive number, and x is the input.
Step 6: Notice the behavior of exponential functions as x becomes very negative (x approaches negative infinity). The output (y) gets closer to 0 but never actually becomes 0.
Step 7: Conclude that exponential functions are the type of functions that have graphs which approach the x-axis but never touch it.

No concepts available.